我们利用代数曲线和Luscher μ项计算了AdS_4 x CP ^3的SU（2）x SU（2）扇区中巨磁振子色散关系的首阶有限尺寸修正。我们考虑单个磁振子以及每个SU（2）中的一个磁振子。此外，将代数曲线计算推广到SU（2）× SU（2）扇区中任意多磁振子态的首阶修正。
英文摘要：
We use the algebraic curve and Luscher's mu-term to calculate the leading order finite size corrections to the dispersion relation of giant magnons in the SU(2) x SU(2) sector of AdS_4 x CP^3. We consider a single magnon as well as one magnon in each SU(2). In addition the algebraic curve computation is generalized to give the leading order correction for an arbitrary multi-magnon state in the SU(2) x SU(2) sector.
We obtain explicit formulas for the eight bosonic and eight fermionic fluctuations around the mixed-flux generalization of the Hofman-Maldacena giant magnon on AdS$_3 \times$S$^3 \times$T$^4$ and AdS$_3 \times$S$^3 \times$S$^3 \times$S$^1$. As a check of our results, we confirm that the semiclassical quantization of these fluctuations leads to a vanishing one-loop correction to the magnon energy, as expected from symmetry based arguments.
Dyonic Giant Magnons in CP^3: Strings and Curves at Finite J
本文用弦σ模型和代数曲线研究了AdS_4 x CP^3中的巨磁振子。我们通过找到CP ^1弦解的双音推广（它与代数曲线中的“小”巨磁振子相匹配），并指出最近用dressing方法构造的解是“大”巨磁振子，来完成解的字典。然后，我们使用的曲线来计算有限J修正的所有情况下，这对于非双音的情况下总是匹配AFZ的结果。对于双介子RP^3磁振子，我们恢复了S^5的答案，但是对于“小”和“大”的巨磁振子，我们得到了新的修正。
The analogues of giant magnon configurations are studied on the string world sheet in the lambda background. This is a discrete deformation of the AdS(5)xS(5) background that preserves the integrability of the world sheet theory. Giant magnon solutions are generated using the dressing method and their dispersion relation is found. This reduces to the usual dyonic giant magnon dispersion relation in the appropriate limit and becomes relativistic in another limit where the lambda model becomes the generalized sine-Gordon theory of the Pohlmeyer reduction. The scattering of giant magnons is then …
The present Letter derives multispin nonrelativistic magnon spectrum considering various near BPS corners within $ SU(1,2|3) $ Spin-Matrix theory (SMT) limit of strings on $ AdS_5 \times S^5 $. In particular, we focus on some typical rotating string solutions those correspond to two spin as well as three spin configurations in the bulk and identify the associated nonrelativistic magnon like excitations in these models.
We explicitly construct the four and two fermion zero modes for the mixed-flux generalization of the Hofman-Maldacena giant magnon on two of the AdS$_3$ backgrounds with maximal amount of supersymmetry, AdS$_3 \times$S$^3 \times$T$^4$ and AdS$_3 \times$S$^3 \times$S$^3 \times$S$^1$. We also show how to get the $\mathfrak{psu}(1|1)^4$ and $\mathfrak{su}(1|1)^2$ superalgebras from the semiclassically quantized fermion zero modes.
We studied the finite-size giant magnons in $\text{AdS}_4\times\text{CP}^3_β$ background using the classical spectral curve constructed in this paper. We computed the finite-size corrections to the dispersion relations for the $RP^3$ giant magnons using our twisted algebraic curve based on the method proposed in arXiv:0810.1246, in which the authors computed the finite-size corrections of giant magnons in $\text{AdS}_4\times\text{CP}^3$ by introducing a finite-size resolvent $G_{\text{finite}}(x)$. We obtained exactly the same result as in arXiv:1106.3686, where a totally different approach wa…
We study classical solutions to the Nambu-Goto string on $AdS_2 \times S^1$ and $AdS_3 \times S^1$ corresponding to strings stretched between wrapped branes extending in $AdS$. The solutions are obtained by analytic continuation of giant magnon solutions, cut at the position of the branes. These solutions carry one or two $SO(2,4)$ charges and a single $SO(6)$ charge. We compute their energies and show their relation to $\frac{1}{2}$-BPS geometries. Their relevance to the $SL(2)$ sector of $\mathcal{N}=4$ SYM is also discussed.
In this paper we have found a classical giant magnon-like solution with both infinite and finite angular momentum moving in Sch_5 x S^5 with B-field, which is believed to be dual to dipole-deformed N=4 super Yang-Mills theory. This string state propagates as a point particle in non-trivial subspace of the Sch_5 space but shows a giant magnon-like property in the S^2 subspace. We derive the energy-momentum dispersion relations and their finite-size correction for the case of finite but large angular momentum.
We show nonrelativistic (NR) giant magnon dispersion relations by probing the torsional Newton Cartan (TNC) geometry with (semi)classical nonrelativistic rigidly rotating strings. We construct NR sigma models over $ R \times S^2 $ and consider two specific limiting cases those are of particular interest. Both of these limiting conditions give rise to what we identify as the \emph{small} momentum limit of the giant magnon dispersion relation in the dual SMT at \emph{strong} coupling. We further generalize our results in the presence of background NS-NS fluxes. Our analysis reveals that unlike i…
Quantum finite-size effects for dyonic magnons in the AdS_4 x CP^3
我们用两种不同的方法计算了AdS_4 x CP^3中各种双子巨磁振子对有限尺寸效应的量子修正。用离壳代数曲线方法对经典弦构型进行了半经典化，并计算了弦能量的修正。这些结果与基于AdS_4 / CFT_3的S-矩阵的F-项Lüscher公式进行了比较。这两个结果的精确匹配为全圈可积猜想和基于全圈可积猜想的精确S-矩阵提供了又一个严格的检验。
